主 讲 人 ：Felix Gotti    研究员

活动时间：2025-09-21 14:30:00

地      点 ：数学科学学院D203报告厅(Zoom: https://us06web.zoom.us/j/86763384947?pwd=qXhOzOcHvaaiw2jqADI8iqNavdgm14.1, ID: 86763384947; passcode: 612593)

主办单位：数学科学学院

讲座内容：

A commutative monoid or domain is said to possess the MCD property if every non-empty finite subset admits a maximal common divisor (MCD). It is well known that monoids satisfying the ascending chain condition on principal ideals (ACCP) necessarily have the MCD property. Although atomicity does not, in general, ascend to polynomial domains, it does ascend when restricted to the class of MCD domains (Roitman, 1993). The behavior of atomicity with respect to power monoids parallels this phenomenon, and we will discuss this in more detail during the first part of the talk.

On the other hand, we say that a commutative monoid has the MCD-finite property if every non-empty finite subset admits only finitely many MCDs (up to associates). Similar to atomicity, the IDF property does not, in general, ascend to polynomial domains (Malcolmson-Okoh, 2009). Nevertheless, the IDF property does ascend to polynomial domains when restricted to the class of MCD-finite domains (Eftekhari-Khorsandi, 2018). In the second part of the talk, we will examine the ascent of the IDF property to power monoids.

主讲人介绍：

Felix Gotti is a lecturer and researcher at the Massachusetts Institute of Technology. He earned his PhD in Mathematics from UC Berkeley in 2019. His research primarily focuses on commutative algebra, semigroup theory, and combinatorics. He also serves as the research coordinator of MIT-PRIMES and as lead research mentor for CrowdMath, programs designed for highly motivated young students conducting mathematical research. He is an editor for Communications in Algebra and has published approximately 40 papers in a range of international journals, including Proc. Amer. Math. Soc., J. Combin. Theory Ser. A, and J. Algebra.